a b s t r a c tThere is a burgeoning literature using non-parametric frontier methods to measure mutual fund performance. These articles measure the relationship between the various characteristics (mainly return information and some costs of ownership) of these specialized financial products to establish a ranking using some efficiency measure. We argue in favor of the use of the shortage function, which is compatible with general investor preferences, and question some of the often maintained hypotheses in this line of research. The empirical part employs a large database of US and European mutual funds to offer extensive tests of the underlying modeling assumptions using various frontier estimators.

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The literature suggests that investors prefer portfolios based on mean, variance and skewness rather than portfolios based on mean-variance (MV) criteria solely. Furthermore, a small variety of methods have been proposed to determine meanvariance-skewness (MVS) optimal portfolios. Recently, the shortage function has been introduced as a measure of efficiency, allowing to characterize MVS optimal portfolios using non-parametric mathematical programming tools. While tracing the MV portfolio frontier has become trivial, the geometric representation of the MVS frontier is an open challenge. A hitherto unnoticed advantage of the shortage function is that it allows to geometrically represent the MVS portfolio frontier. The purpose of this contribution is to systematically develop geometric representations of the MVS portfolio frontier using the shortage function and related approaches.

The need to adapt Data Envelopment Analysis (DEA) and other frontier models in the context of negative data has been a rather neglected issue in the literature. Silva Portela, Thanassoulis, and Simpson ( 2004) proposed a variation on the directional distance function, a very general distance function that is dual to the profit function, to accommodate eventual negative data. In this contribution, we suggest a simple variation on the proportional distance function that can do the same job.